1. What is the Inscribed Angle Theorem?

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. This fundamental geometric principle helps in solving various circle-related problems.

2. How Does the Calculator Work?

The calculator uses the Inscribed Angle Theorem:

Where:

• Inscribed — The measure of the inscribed angle (degrees)
• arc_var — The measure of the intercepted arc (degrees)

Explanation: The calculator simply divides the arc measurement by 2 to find the inscribed angle.

3. Importance of Inscribed Angles

Details: Understanding inscribed angles is crucial for solving geometry problems involving circles, including finding arc lengths, chord lengths, and other angle measures.

4. Using the Calculator

Tips: Enter the arc measurement in degrees. The value must be positive and less than or equal to 360 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is an inscribed angle?
A: An inscribed angle is an angle formed by two chords in a circle which have a common endpoint on the circle.

Q2: What is an intercepted arc?
A: The arc that lies between the two chords that form the inscribed angle is called the intercepted arc.

Q3: Does the position of the angle matter?
A: No, as long as the vertex is on the circle and the sides are chords, the theorem applies.

Q4: What if the arc is more than 180 degrees?
A: The theorem still applies, but the inscribed angle will be more than 90 degrees.

Q5: Can this be used for tangent-chord angles?
A: No, this calculator is specifically for angles formed by two chords (inscribed angles).